TSTP Solution File: GRP485-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP485-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 11:47:42 EDT 2022

% Result   : Unsatisfiable 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   48 (  48 unt;   0 nHn;  48 RR)
%            Number of literals    :   48 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,v),w),double_divide(v,identity))),double_divide(identity,identity)),w),
    file('GRP485-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP485-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP485-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP485-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(identity,a2),a2),
    file('GRP485-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(7,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,v),w),inverse(v))),inverse(identity)),w),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0,3.0,1.0')] ).

cnf(10,plain,
    equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

cnf(12,plain,
    equal(multiply(inverse(u),u),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[4,6]),
    [iquote('0:SpR:4.0,6.0')] ).

cnf(13,plain,
    equal(multiply(identity,u),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpR:3.0,6.0')] ).

cnf(14,plain,
    ~ equal(inverse(inverse(a2)),a2),
    inference(rew,[status(thm),theory(equality)],[13,5]),
    [iquote('0:Rew:13.0,5.0')] ).

cnf(16,plain,
    equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[6,12]),
    [iquote('0:SpR:6.0,12.0')] ).

cnf(54,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),inverse(identity))),inverse(identity)),v),
    inference(spr,[status(thm),theory(equality)],[3,7]),
    [iquote('0:SpR:3.0,7.0')] ).

cnf(57,plain,
    equal(double_divide(double_divide(u,double_divide(inverse(double_divide(u,v)),inverse(v))),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[3,7]),
    [iquote('0:SpR:3.0,7.0')] ).

cnf(58,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(v,u)),
    inference(spr,[status(thm),theory(equality)],[10,7]),
    [iquote('0:SpR:10.0,7.0')] ).

cnf(60,plain,
    equal(double_divide(double_divide(u,double_divide(multiply(v,u),inverse(v))),inverse(identity)),identity),
    inference(rew,[status(thm),theory(equality)],[6,57]),
    [iquote('0:Rew:6.0,57.0')] ).

cnf(69,plain,
    equal(double_divide(double_divide(u,multiply(v,double_divide(u,identity))),inverse(identity)),double_divide(identity,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[58,7]),
    [iquote('0:SpR:58.0,7.0')] ).

cnf(73,plain,
    equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[4,58]),
    [iquote('0:SpR:4.0,58.0')] ).

cnf(74,plain,
    equal(double_divide(inverse(u),inverse(identity)),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[3,73,13]),
    [iquote('0:Rew:3.0,73.0,13.0,73.0')] ).

cnf(76,plain,
    equal(double_divide(double_divide(u,multiply(v,inverse(u))),inverse(identity)),double_divide(identity,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[3,69]),
    [iquote('0:Rew:3.0,69.0')] ).

cnf(79,plain,
    equal(multiply(inverse(identity),inverse(u)),inverse(inverse(inverse(u)))),
    inference(spr,[status(thm),theory(equality)],[74,6]),
    [iquote('0:SpR:74.0,6.0')] ).

cnf(84,plain,
    equal(double_divide(multiply(u,v),inverse(identity)),inverse(multiply(u,v))),
    inference(spr,[status(thm),theory(equality)],[6,74]),
    [iquote('0:SpR:6.0,74.0')] ).

cnf(108,plain,
    equal(double_divide(multiply(u,double_divide(v,identity)),inverse(u)),double_divide(double_divide(v,identity),inverse(identity))),
    inference(spr,[status(thm),theory(equality)],[60,7]),
    [iquote('0:SpR:60.0,7.0')] ).

cnf(116,plain,
    equal(double_divide(double_divide(u,inverse(multiply(identity,u))),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[84,60]),
    [iquote('0:SpR:84.0,60.0')] ).

cnf(117,plain,
    equal(double_divide(double_divide(u,inverse(inverse(inverse(u)))),inverse(identity)),identity),
    inference(rew,[status(thm),theory(equality)],[13,116]),
    [iquote('0:Rew:13.0,116.0')] ).

cnf(120,plain,
    equal(double_divide(multiply(u,inverse(v)),inverse(u)),inverse(inverse(v))),
    inference(rew,[status(thm),theory(equality)],[74,108,3]),
    [iquote('0:Rew:74.0,108.0,3.0,108.0')] ).

cnf(128,plain,
    equal(double_divide(double_divide(u,identity),inverse(identity)),inverse(inverse(inverse(double_divide(u,identity))))),
    inference(spr,[status(thm),theory(equality)],[117,7]),
    [iquote('0:SpR:117.0,7.0')] ).

cnf(133,plain,
    equal(inverse(inverse(inverse(inverse(u)))),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[74,128,3]),
    [iquote('0:Rew:74.0,128.0,3.0,128.0')] ).

cnf(148,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(inverse(v)))),inverse(identity)),multiply(inverse(inverse(inverse(v))),u)),
    inference(spr,[status(thm),theory(equality)],[133,58]),
    [iquote('0:SpR:133.0,58.0')] ).

cnf(155,plain,
    equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),v)),
    inference(rew,[status(thm),theory(equality)],[58,148]),
    [iquote('0:Rew:58.0,148.0')] ).

cnf(204,plain,
    equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[120,6]),
    [iquote('0:SpR:120.0,6.0')] ).

cnf(207,plain,
    equal(multiply(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(v))),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[120,16]),
    [iquote('0:SpR:120.0,16.0')] ).

cnf(228,plain,
    equal(multiply(inverse(u),inverse(inverse(u))),inverse(identity)),
    inference(rew,[status(thm),theory(equality)],[155,207,204]),
    [iquote('0:Rew:155.0,207.0,204.0,207.0')] ).

cnf(234,plain,
    equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[228,79]),
    [iquote('0:SpR:228.0,79.0')] ).

cnf(236,plain,
    equal(double_divide(inverse(identity),inverse(inverse(u))),inverse(inverse(inverse(u)))),
    inference(spr,[status(thm),theory(equality)],[228,120]),
    [iquote('0:SpR:228.0,120.0')] ).

cnf(242,plain,
    equal(inverse(inverse(identity)),inverse(identity)),
    inference(rew,[status(thm),theory(equality)],[133,234]),
    [iquote('0:Rew:133.0,234.0')] ).

cnf(256,plain,
    equal(double_divide(inverse(identity),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[242,4]),
    [iquote('0:SpR:242.0,4.0')] ).

cnf(276,plain,
    equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[242,256,74]),
    [iquote('0:Rew:242.0,256.0,74.0,256.0')] ).

cnf(289,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),identity)),identity),v),
    inference(rew,[status(thm),theory(equality)],[276,54]),
    [iquote('0:Rew:276.0,54.0')] ).

cnf(296,plain,
    equal(double_divide(double_divide(u,multiply(v,inverse(u))),identity),double_divide(identity,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[276,76]),
    [iquote('0:Rew:276.0,76.0')] ).

cnf(314,plain,
    equal(double_divide(identity,inverse(inverse(u))),inverse(inverse(inverse(u)))),
    inference(rew,[status(thm),theory(equality)],[276,236]),
    [iquote('0:Rew:276.0,236.0')] ).

cnf(356,plain,
    equal(multiply(multiply(u,inverse(v)),v),u),
    inference(rew,[status(thm),theory(equality)],[6,289,3]),
    [iquote('0:Rew:6.0,289.0,3.0,289.0,6.0,289.0,3.0,289.0')] ).

cnf(364,plain,
    equal(multiply(multiply(u,inverse(v)),v),double_divide(identity,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[6,296,3]),
    [iquote('0:Rew:6.0,296.0,3.0,296.0')] ).

cnf(365,plain,
    equal(double_divide(identity,inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[356,364]),
    [iquote('0:Rew:356.0,364.0')] ).

cnf(367,plain,
    equal(inverse(inverse(inverse(u))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[365,314]),
    [iquote('0:Rew:365.0,314.0')] ).

cnf(475,plain,
    equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[367,365]),
    [iquote('0:SpR:367.0,365.0')] ).

cnf(484,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[365,475]),
    [iquote('0:Rew:365.0,475.0')] ).

cnf(485,plain,
    $false,
    inference(unc,[status(thm)],[484,14]),
    [iquote('0:UnC:484.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : GRP485-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.11  % Command  : run_spass %d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Mon Jun 13 22:44:27 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.15/0.38  
% 0.15/0.38  SPASS V 3.9 
% 0.15/0.38  SPASS beiseite: Proof found.
% 0.15/0.38  % SZS status Theorem
% 0.15/0.38  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.15/0.38  SPASS derived 299 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.15/0.38  SPASS allocated 63665 KBytes.
% 0.15/0.38  SPASS spent	0:00:00.06 on the problem.
% 0.15/0.38  		0:00:00.02 for the input.
% 0.15/0.38  		0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.38  		0:00:00.00 for inferences.
% 0.15/0.38  		0:00:00.00 for the backtracking.
% 0.15/0.38  		0:00:00.02 for the reduction.
% 0.15/0.38  
% 0.15/0.38  
% 0.15/0.38  Here is a proof with depth 7, length 48 :
% 0.15/0.38  % SZS output start Refutation
% See solution above
% 0.15/0.38  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.15/0.38  
%------------------------------------------------------------------------------